Old Sextic Fields Unramified Outside of {∞, 5, 11}

Discriminant class: −55

∞ 5 11 a_{1} a_{2} a_{3} Over p = 5  Over p = 11  2 3 7 13 17 19 23 29
G h  a_{4} a_{5} a_{6} f^{e} c_{w} d s f^{e} c_{w} d  s 31 37 41 43 47 53 59 61
1. 3_{i} 9_{−} 3_{i} -1 5 -10 1^{5} 9_{−} 5  2^{2} 2_{+} 1  V 5 6 33 22 5 4 4 222
S_{5} 2  0 2 23  1^{2} 1_{i} 11∗ 11∗ 33 222 6 5 6 4 22 6
2. 3_{i} 9_{−} 5_{i} -1 5 -50 1^{5} 9_{−} 5  1^{6} 5_{i} 11∗  5 4 5 5 5 6 222 222
S_{5} 2  20 6 559  5 4 4 22 6 4 33 222

Discriminant class: −11

∞ 5 11 a_{1} a_{2} a_{3} Over p = 5  Over p = 11  2 3 7 13 17 19 23 29
G h  a_{4} a_{5} a_{6} f^{e} c_{w} d s f^{e} c_{w} d  s 31 37 41 43 47 53 59 61
3. 3_{i} 6_{+} 3_{k} -1 -5 10 1^{5} 6_{+} 1  1^{4} 3_{k} 11 11∗ 6 5 222 4 4 6 5 4
S_{5} 10 -19 9 2 0_{+} ∗ ∗ 33 33 6 4 33 5 33 6

Discriminant class: 5

∞ 5 11 a_{1} a_{2} a_{3} Over p = 5  Over p = 11 2 3 7 13 17 19 23 29
G h  a_{4} a_{5} a_{6} f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
4. 2_{−} 5_{−} 4_{+} -1 0 -10 1^{5} 5_{−} 5  1^{3} 2_{+} ∗  6 6 4 4 222 5 6 5
S_{5}  0 8 7  1^{3} 2_{+} ∗  5 4 22 222 4 4 33 33
5. 2_{−} 9_{−} 4_{+} -2 -5 20 1^{5} 9_{−} 5  1^{5} 4_{+} 1  6 222 222 6 6 5 4 5
S_{5}  -25 -41 107  5 4 5 4 4 6 5 22